Making a realistic dust trail
It's amazingly easy to achieve.


Create emitter with Real World Scale - this is important, as Smoke sim can differ based on scale. Mine has ~56x7m. Apply Scale! 
Add to it Quick Smoke - F3 > Quick Smoke.
Scale Domain in Edit Mode to make it as big as you need. 
In Domain settings I've changed only Resolution - 192, Temp. Diff. - -0.04, Adaptive Domain - checked and High Resolution - checked + Resolution Division > 2.


Collision Object. This is most important thing to do here. Set it as Smoke > Collision and Animated.



Now you have 3 options how to interact with smoke. 


Allow object to "sink" into smoke.
Attach to object "plow" to raise smoke and not be visible in Render.
Attach Force Field to object to "suck" smoke from the ground.



This is it for the Smoke sim. You can cover smoke after baking by ground material, it will only show after being forced up.

Also to produce something as realistic as from your reference smoke is not enough. You can add some Particles for bigger parts from the ground (not necessary), motion blur, colors for the volume and probably that's it.